one-way versus two-way infinite sequences

[Michael Somos]

seqfan,

     Currently we have a situation where some sequences in OEIS
are implicity two-way infinite while the great majority are only
one-way infinite. The problem for me is that there is no indication
of which sequences are two-way infinite. One can guess from context
which ones might be two-way, but one can guess wrong. But if the
two-way infinite sequences have generating functions, then is that
the generating function of the two-way sequence or only the one-way
version which is indicated by the sequence values? For example:

%S A000035 0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,
%N A000035 A simple periodic sequence. Least significant bit of n, lsb(n).
%K A000035 core,easy,nonn,nice,mult

There is no indication that the pattern continues for negative
values of n. One can guess from 

%F A000035 a(n)={1 - (-1)^n}/2. a(n) = n mod 2.

that it does, but formulas have been wrong before. Just to give a
non-trivial example, what about :

%S A000003 1,1,1,1,2,2,1,2,2,2,3,2,2,4,2,2,4,2,3,4,4,2,3,4,2,6,3,2,6,4,3,4,4,4,
%N A000003 Classes of primitive binary forms of discriminant D=-4n;
%K A000003 nonn,nice,easy

Does this sequence also include negative n? One can investigate and
determine if this is possible, but nothing in the entry indicates
that this is excluded or not. I could give many other examples, but
this is enough for now. Shalom, Michael